Existence and stability of the resonant phenomena in the dc- and ac-driven overdamped Frenkel-Kontorova model with the incommensurate structure.

Dynamical mode-locking phenomena in the incommensurate structures of the dc- and ac-driven overdamped Frenkel-Kontorova model are studied by molecular-dynamics simulations. The obtained results have shown that Shapiro steps exhibit significantly different amplitude and frequency dependence from the one observed in the commensurate structures. Due to the incommensurability of the system the special symmetry of the motion of particles is broken, and in the amplitude dependence of Shapiro steps, this will result in the appearance of anomalies and deviation from the well-known Bessel-like behavior. In the frequency or period dependence, oscillations have been observed in the high-amplitude limit; however, they exhibit strong anomalies compared with those in the commensurate structures. The oscillatory behavior and the anomalies have been also be revealed in the (F(ac),F) and the (ν(0),F) phase diagrams where several phases are defined.